Hello Attila
Typically, the best practice in today’s networking environment is to leave the duplex and speed settings at their default. This is especially true if you are using the same vendor for your networking equipment across your whole network.
Concerning duplex settings, they are only meaningful for Ethernet and FastEthernet (10 and 100 Mbps, respectively), and even then, they should negotiate to full duplex since both technologies are capable of that. Only under special circumstances should you change it, such as when connecting devices that don’t support full duplex or don’t support auto-negotiation.
Concerning the speed, I would also not recommend changing the default because, on a large network, there are often cases when a device will be capable of FastEthernet only and will need to be specially accommodated to get it to work. It’s adding one more step to resolve issues that would not exist if the default was kept.
Working on large networks with thousands of access ports, with the duplex and speed configs set to their defaults, I have never come across a problem with duplex or speed mismatches. If you have a consistency of vendor throughout, it is even more unlikely you will ever come across it. So it is best in my opinion to leave it as it is, and any rare problems that may occur due to old equipment or unsupported auto-negotiation can be dealt with on a case-by-case basis.
The point of the lesson is to ensure that we understand the concepts involved with speed and duplex settings.
As for routers, the behavior is the same as far as duplex and speed settings on the interfaces go.
I hope this has been helpful!
Laz